The 5000-gal aquarium is maintained with the pumping system which passes 100 gal of water per minute through tank. To treat the certain fish malady, the soluble antibiotic is introduced into inflow system. Suppose that inflow concentration of medicine is 10te^(-t/50) mg/gal, where t is estimated in minutes. Well-stirred mixture flows out of aquarium at same rate.
i) How much medicine is in tank at any time t>= 0.
ii) Find maximum concentration of medicine attained by dosing and when it occurs?
iii) For antibiotic to be effective, its concentration should exceed 100 mg/gal for the minimum of 60 min. Was dosing effective?